# Roland Bauerschmidt

I am a postdoctoral member of the School of Mathematics at the Institute for Advanced Study in Princeton.

E-mail address: brt at the same domain as this webpage

School of Mathematics
Einstein Drive
Princeton, NJ, 08540 USA
Telephone: +1-609-734-8080

## Research in mathematics

My mathematical research interest is in probability theory and analysis, in particular in their applications to statistical mechanics. I am especially interested in multiscale and renormalization group methods. Before coming to Princeton, I obtained my Ph.D. degree in the Probability Theory Group at the University of British Columbia in Vancouver. My supervisors were Gordon Slade and David Brydges. I have obtained my B.Sc. and M.Sc. degrees in physics from ETH Zürich. My master's thesis was supervised by Jürg Fröhlich and Wojciech de Roeck.

### In preparation

• Logarithmic corrections for the susceptibility of the 4-dimensional weakly self-avoiding walk: a renormalisation group analysis
R. Bauerschmidt, D.C. Brydges, and G. Slade
Summary: For the continuous-time weakly self-avoiding walk in dimension four, we prove that the susceptibility has a logarithmic correction to the mean-field scaling behavior with exponent 1/4 for the logarithm. This exponent has been predicted in the physics literature and are conjectured to be universal for four dimensional self-avoiding walks. The analysis uses a rigorous renormalization group method developed by Brydges and Slade.
• Linear polymers with self-attraction in dimension four and higher
R. Bauerschmidt, D.C. Brydges, and G. Slade
Summary: The self-avoiding walk is a basic model for a long molecule chain in a good solution. The self-avoidance constraint models the volume effect of the polymer. In a poor solution, there are two competing forces, a repelling one that models the volume effect of the polymer, and an attractive force that accounts for the fact that the polymer tries to avoid contact with the solution. We show that the renormalization group method for the weakly self-avoiding walk developed by Brydges and Slade can be extended to show that, in four dimensions, the two-point function has mean-field behavior in a region of the extended phase of the polymer.

### Completed manuscripts (preprints)

 Structural stability of a dynamical system near a non-hyperbolic fixed point R. Bauerschmidt, D.C. Brydges, and G. Slade Revised version will appear in Annales Henri Poincaré. A simple method for finite range decomposition of quadratic forms and Gaussian fields R. Bauerschmidt To appear in Probability Theory and Related Fields. Lectures on Self-Avoiding Walks R. Bauerschmidt, H. Duminil-Copin, J. Goodman, and G. Slade Probability and Statistical Physics in Two and More Dimensions, Clay Mathematics Proceedings, vol. 15, Amer. Math. Soc., 2010, pp. 395-476

### Related slides

 Finite range decomposition of Green's functions McGill University Analysis Seminar

## Miscellaneous

My favorite author is Paul Auster.